Norm retrieval and phase retrieval by projections

Phaseless Sampling and Reconstruction of Real-Valued Signals in Shift-Invariant Spaces

“…The local complement property on a bounded open set can be characterized by phase retrievable frames associated with the generator Φ and the sampling set Γ on a finitedimensional space, see Proposition 5.4. The reader may refer to [3,4,9,10,11,18,21,23,31,43] and references therein for historical remarks and recent advances on finite-dimensional phase retrievable frames.…”

“…Even in the finite-dimensional setting, there are still lots of mathematical and engineering problems about phase retrieval unanswered. The reader may refer to [7,8,13,14,15,25,28,32,39] and references therein for historical remarks and recent advances.…”

“…11) and applying (3.12), there existδ λ ∈ {−1, 1}, λ ∈ Λ such that (3.13) d λ = δ λ c λ for all λ ∈ Λ, and (3.14) δ λ = δ λ for any edge (λ, λ ) in the graph G f . Combining (3.13) and (3.14), and applying connectivity of the graph G f , we can find δ ∈ {−1, 1} such that (3.15) d λ = c λ = 0 for all λ ∈ V f and d λ = δc λ for all λ ∈ V f .…”